Quantum Tic-Tac-Toe as Metaphor for Quantum Physics
Allan Goff
Quantum Tic‐Tac‐Toe is presented as an abstract quantum system derived from the rules of Classical Tic‐Tac‐Toe. Abstract quantum systems can be constructed from classical systems by the addition of three types of rules; rules of Superposition, rules of Entanglement, and rules of Collapse. This is formally done for Quantum Tic‐Tac‐Toe. As a part of this construction it is shown that abstract quantum systems can be viewed as an ensemble of classical systems. That is, the state of a quantum game implies a set of simultaneous classical games. The number and evolution of the ensemble of classical games is driven by the superposition, entanglement, and collapse rules. Various aspects and play situations provide excellent metaphors for standard features of quantum mechanics. Several of the more significant metaphors are discussed, including a measurement mechanism, the correspondence principle, Everett’s Many Worlds Hypothesis, an ascertainity principle, and spooky action at a distance. Abstract quantum systems also show the consistency of backwards‐in‐time causality, and the influence on the present of both pasts and futures that never happened. The strongest logical argument against faster‐than‐light (FTL) phenomena is that since FTL implies backwards‐in‐time causality, temporal paradox is an unavoidable consequence of FTL; hence FTL is impossible. Since abstract quantum systems support backwards‐in‐time causality but avoid temporal paradox through pruning of the classical ensemble, it may be that quantum based FTL schemes are possible allowing backwards‐in‐time causality, but prohibiting temporal paradox.
AIP conference proceedings•Jan 1, 2004•4 citations